Danny Long

North Carolina State University
Graduate Teaching Assistant

Biography

Taught Calculus I for Engineers, Calculus for Biological Scientists, and Matlab.

Education

BS Applied Mathematics
North Carolina State University
Phd Mathematics
Colorado State University

Educator Statistics

Numerade tutor for 6 years
18 Students Helped

Topics Covered

Mastering Integrals: Tips and Tricks for Calculus Success
Integration
Mastering Integration Techniques for Optimal Results
Applications of Integration: Exploring Real-World Solutions

Danny's Textbook Answer Videos

05:13
Thomas Calculus

Air pollution A power plant generates electricity by burning oil.
Pollutants produced as a result of the burning process are removed
by scrubbers in the smokestacks. Over time, the scrubbers
become less efficient and eventually they must be replaced when the amount of pollution released exceeds government standards.
Measurements are taken at the end of each month determining the
rate at which pollutants are released into the atmosphere, recorded
as follows.
a. Assuming a $30-$ day month and that new scrubbers allow only
0.05 ton/day to be released, give an upper estimate of the
total tonnage of pollutants released by the end of June. What is
a lower estimate?
b. In the best case, approximately when will a total of 125 tons
of pollutants have been released into the atmosphere?

Chapter 5: Integrals
Section 1: Area and Estimating with Finite Sums
Danny Long
04:14
Thomas Calculus

Find the lengths of the curves in Exercises $1-12 .$ If you have graphing
software, you may want to graph these curves to see what they look
like.
$$y=x^{3 / 2} \text { from } x=0 \text { to } x=4$$

Chapter 6: Applications of Definite Integrals
Section 3: Arc Length
Danny Long
07:36
Thomas Calculus

Find the lengths of the curves in Exercises $1-12 .$ If you have graphing
software, you may want to graph these curves to see what they look
like.
$$x=\left(y^{3 / 2} / 3\right)-y^{1 / 2} \text { from } y=1 \text { to } y=9$$

Chapter 6: Applications of Definite Integrals
Section 3: Arc Length
Danny Long
05:54
Thomas Calculus

Find the lengths of the curves in Exercises $1-12 .$ If you have graphing
software, you may want to graph these curves to see what they look
like.
$$x=\left(y^{3} / 6\right)+1 /(2 y) \quad \text { from } \quad y=2 \text { to } y=3$$

Chapter 6: Applications of Definite Integrals
Section 3: Arc Length
Danny Long
07:25
Thomas Calculus

Find the lengths of the curves in Exercises $1-12 .$ If you have graphing
software, you may want to graph these curves to see what they look
like.
$$y=\left(x^{3} / 3\right)+x^{2}+x+1 /(4 x+4), \quad 0 \leq x \leq 2$$

Chapter 6: Applications of Definite Integrals
Section 3: Arc Length
Danny Long
03:45
Thomas Calculus

Find the lengths of the curves in Exercises $1-12 .$ If you have graphing
software, you may want to graph these curves to see what they look
like.
$$y=\frac{x^{5}}{5}+\frac{1}{12 x^{3}}, \quad \frac{1}{2} \leq x \leq 1$$

Chapter 6: Applications of Definite Integrals
Section 3: Arc Length
Danny Long
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